The following code must be inserted in the function.php contained in your child theme (**).

/*  This  code shows the Category of a woocommerce product */

add_action('wp_head', 'get_current_product_category');

function get_current_product_category(){
	global $post;
$terms = get_the_terms( $post->ID, 'product_cat' );        
if($terms) {
		foreach ($terms as $term){
		    $product_cat_id = $term->term_id;
		    $product_cat_name = $term->name;
		   
		    break;
		
			
		}
}
 echo $product_cat_name ."  " . $product_cat_id  ;

}

(**) How to Create a Child Theme

A child theme is a theme that inherits the functionality and styling of another theme, called the parent theme. Child themes are the recommended way of modifying an existing theme.

  1. Create child theme directory (common approach to name child theme as the parent theme plus -child added on the end.)
  2. Create style.css
  3. Create functions.php

For more detailed instructions on child themes you can visit the following links:

https://developer.wordpress.org/themes/advanced-topics/child-themes/

https://blog.hubspot.com/website/wordpress-create-child-theme